Choice
f is both continuous and differentiable at x = 0
f '(x) exists for all x except x = 0 f is not continuous at x = 0
f '(x) is continuous for all x
f '(x) does not exist anywhere
f '(x) exists for all x but is not continuous for all x
f is continuous at x = 0 but not differentiable at x = 0
Number of available correct choices: 2

Choice
f is both continuous and differentiable at x = 0
f '(x) exists for all x except x = 0 f is not continuous at x = 0
f '(x) is continuous for all x
f '(x) does not exist anywhere
f '(x) exists for all x but is not continuous for all x
f is continuous at x = 0 but not differentiable at x = 0
Number of available correct choices: 2